Time Series Trend Calculator
Estimate a linear trend from time-series data using the slope of the regression line over time periods.
Trend Slope (per period)
7.2000
Trend Slope (per period) vs Period 1 Value
Formula
## How to Estimate a Time Series Trend ### Method Fit a least-squares regression line Y = a + b*t where t is the time period (1, 2, 3, ...). The slope b is the average change per period. The intercept a is the estimated value at t=0. Extrapolating the line gives forecasts for future periods. **Slope b = [n*Sum(t*y) - Sum(t)*Sum(y)] / [n*Sum(t^2) - (Sum(t))^2]**
Exemplo Resolvido
Five periods with values 100, 108, 115, 120, 130.
- 01Sum(y) = 573, Sum(t) = 15, Sum(t^2) = 55
- 02Sum(t*y) = 1*100 + 2*108 + 3*115 + 4*120 + 5*130 = 1791
- 03Slope = (5*1791 - 15*573) / (5*55 - 225) = (8955-8595)/50 = 7.2
- 04Intercept = (573 - 7.2*15)/5 = (573 - 108)/5 = 93
- 05Forecast for period 6: 93 + 7.2*6 = 136.2
Perguntas Frequentes
What does the trend slope represent?
The slope is the average change per time period. A slope of 7.2 means the value increases by about 7.2 units per period on average. Negative slope indicates a declining trend.
Is a linear trend always appropriate?
No. Many real-world time series exhibit nonlinear trends (exponential growth, logistic curves, cyclical patterns). Plot the data first. If the trend curves, consider log transforms or polynomial/exponential models.
How reliable are trend extrapolations?
Extrapolation becomes less reliable the further you project beyond the data. Short-term forecasts from clear trends are reasonable; long-term extrapolation is risky because conditions change.
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